Of a group scheme

Sometimes the term ‘’order’‘ refers to the height of a (group) schemeXX over a field (of characteristicpp) which is defined to be the dimension of the associated ring of functions O(X)O(X) as a kk-vector space. Another term for this notion is ‘’rank’’. If this group scheme is moreover p-divisible - which means that is is in fact a codirected diagram of group schemes of order pvhp^{v h}; in this case hh is called the order or height of XX.